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- Giorgio Gallo, Michael D. Grigoriadis, Robert E. Tarjan
- SIAM J. Comput.
- 1989

The classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter, and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition. Finding the desired parameter value requires solving a sequence of related… (More)

- Michael D. Grigoriadis, Leonid Khachiyan
- SIAM Journal on Optimization
- 1994

- Michael D. Grigoriadis, Leonid Khachiyan
- Math. Oper. Res.
- 1996

- Michael D. Grigoriadis, Leonid Khachiyan
- Oper. Res. Lett.
- 1995

- Michael D. Grigoriadis, Leonid Khachiyan, Lorant Porkolab, J. Villavicencio
- SIAM Journal on Optimization
- 2001

We present a Lagrangian decomposition algorithmwhich uses logarithmic potential reduction to compute an ε-approximate solution of the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. We show that this algorithm runs in O(M(ε+lnM)) iterations, a data independent bound which is optimal up to polylogarithmic… (More)

- Michael D. Grigoriadis, Leonid Khachiyan
- Networks
- 1995

- Andrew V. Goldberg, Michael D. Grigoriadis, Robert E. Tarjan
- Math. Program.
- 1991

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on an n-vertex, m-arc network in at most nm pivots and O(nZm) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm… (More)

- Michael D. Grigoriadis, Leonid Khachiyan
- Math. Program.
- 1996

We show that an "-approximate solution of the cost-constrained K-commodity ow problem on an N-nodeM-arc network G can be computed by sequentially solving O K(" 2 + logK) logM log(" 1 K) single-commodity minimum-cost ow problems on the same network. In particular, an approximate minimumcost multicommodity ow can be computed in ~ O(" 2 KNM) running time,… (More)

- Michael D. Grigoriadis, Leonid Khachiyan
- SIAM Journal on Optimization
- 1996

This paper presents an interior point method for solving a bordered block-diagonal linear program which consists of a number of disjoint blocks coupled by a total of p variables and constraints. This structure includes the well-known block-angular and dual block-angular structures, as well as their special cases, such as staircase problems, generalized… (More)